Discussion Forum



1)

Let X and Y the two events such  $P(X)=\frac{1}{3}$ , $P(X\mid Y)= \frac{1}{2}$, $P(Y\mid X)= \frac{2}{5}$    Then


A) $P(Y)= \frac{4}{15}$

B) $P(X'\mid Y)= \frac{1}{2}$

C) $P(X\cup Y)= \frac{2}{5}$

D) $P(X\cap Y)= \frac{1}{5}$

Answer:

Option A,B

Explanation:

$P(X)=\frac{1}{3}$

$P(\frac{X}{Y})=\frac{P(X\cap Y)}{P(Y)}=\frac{1}{2}$

$P(\frac{Y}{X})=\frac{P(X\cap Y)}{P(X)}=\frac{2}{5}$

$P(X\cap Y)=\frac{2}{15}$

$P(Y)=\frac{4}{15}$

  $P(\frac{X'}{Y})=\frac{P(Y)-P(X\cap Y)}{P(Y)}$

$=\frac{\frac{4}{15}-\frac{2}{15}}{\frac{4}{15}}=\frac{1}{2}$

$P(X\cup Y)=\frac{1}{3}+\frac{4}{15}-\frac{2}{15}$

   = $\frac{7}{15}=\frac{7}{15}$